Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60753 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#60809 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C17×#117 ◁ G | |
2034 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,23)(22,25)(26,27,32,37)(28,33,39,47)(29,42,44,51)(30,36,31,35)(34,45,50,43)(38,52,53,57)(40,49,41,48)(46,55,56,54);(18,20,21,25)(19,22,23,24)(26,28)(27,33)(29,38)(30,40)(31,41)(32,39)(34,46)(35,48)(36,49)(37,47)(42,52)(43,54)(44,53)(45,55)(50,56)(51,57);(20,25)(22,24)(26,29)(27,34)(28,38)(30,43)(31,45)(32,44)(33,46)(35,42)(36,51)(37,50)(39,53)(40,54)(41,55)(47,56)(48,52)(49,57);(19,23)(22,24)(28,39)(33,47)(38,53)(40,41)(46,56)(48,49)(52,57)(54,55);(26,30,32,31)(27,35,37,36)(28,40,39,41)(29,43,44,45)(33,48,47,49)(34,42,50,51)(38,54,53,55)(46,52,56,57)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53797);